Explanatory note on detection of statistical significance
in long-term trends
Meteorological observation data, including those relating to temperature and precipitation,
are subject to large amplitude fluctuations due to the influence of atmospheric and oceanic
dynamics on a broad spectrum of spatial and temporal scales. To examine the possible presence
of long-term climate system trends associated with global warming in consideration of natural
variability, raw climate data need to be converted into suitable statistical time-series
representations and subjected to statistical testing in order to highlight the likelihood of
systematic temporal trends that cannot be explained by random variability alone. When the
results of such testing allow reasonable conclusion that random variability is unlikely to be the
sole factor at work, a change is described as statistically significant.
In this report, the likelihood of a systematic long-term change existing in a time-series
representation is based on the results of statistical significance testing performed at confidence
levels of 99, 95 and 90%. The following terminology summary describes each level:
Level of
confidence
≥ 99%
≥ 95%
≥ 90%
< 90%
Term
Virtually certain to have increased/decreased (statistically significant at
a confidence level of 99%)
Extremely likely to have increased/decreased (statistically significant at
a confidence level of 95%)
Very likely to have increased/decreased (statistically significant at a
confidence level of 90%)
No discernible trend
The following statistical methods are applied for the data used in this report:
i) For statistical variables whose annual fluctuation component can be assumed to follow
normal distribution
For temperature anomalies, trend-removed annual variability data are expected to
approximately follow normal distribution. T-testing is performed for statistical variables
assumed to be normally distributed using a coefficient of correlation between years and values.
ii) For statistical variables whose annual fluctuation component cannot be assumed to follow
normal distribution
The assumption of normality may not be applicable to frequency statistics regarding weather
conditions, including those for extremely warm days, tropical nights and hourly precipitation
amounts exceeding 50 mm. Accordingly, non-parametric testing, which does not depend on
underlying assumptions about distribution, is applied to such variables.
It should be noted that statistical tests are in theory inevitably susceptible to the establishment
of false conclusions even if the results indicate a statistically significant trend. Even outcomes
indicating statistical significance at confidence levels of 90, 95 or 99% imply that there are
small inherent probabilities of up to 10, 5 and 1%, respectively, of the significance being
erroneously detected when in fact the observed long-term change occurred by mere random
chance. Conversely, when a systematic long-term change actually exists, statistical testing may
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fail to detect the significance correctly. In general, test results are not considered highly stable if
they are based on observation records that are temporally limited, influenced by large annual
fluctuations/rare events or subject to change when new observations are added to a data
sequence. Readers are encouraged to interpret the analytical results presented in the report
appropriately with due note of these considerations.
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